Create a new UV map but move the textures with the polygons?
If the two UV maps reside on the same mesh you can use UV baking. If you create a material with the texture and the first uv layer, you can bake the diffuse color (or even the rendered result, if you make a shadeless material) and bake it to the second UV layer. Make sure to select the proper UV layers in the material texture slot, UV editor and active UV layer.